.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/solutions/acid_base/plot_02_law_of_mass_action.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_solutions_acid_base_plot_02_law_of_mass_action.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_solutions_acid_base_plot_02_law_of_mass_action.py:


Guldberg and Waage's law of mass action: a constant equilibrium quotient
==========================================================================

The law of mass action says that at equilibrium the concentrations of
products and reactants, each raised to its stoichiometric power, combine
into a quotient that is fixed at a given temperature. For
:math:`HA \rightleftharpoons H^+ + A^-`:

.. math::

   K_a = \frac{[H^+][A^-]}{[HA]}.

Below, the equilibrium concentrations of three weak acids are solved
exactly with :class:`~chemistrykit.solutions.systems.acid_base.WeakAcid`
over six decades of total concentration. The individual concentrations
change by orders of magnitude, but the mass-action quotient stays fixed
at :math:`K_a`, while a quotient that is *not* the mass-action form,
such as :math:`[H^+]/[HA]`, does not.

.. GENERATED FROM PYTHON SOURCE LINES 23-54

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.solutions.systems.acid_base import WeakAcid

    acids = {"formic acid": 1.8e-4, "acetic acid": 1.8e-5, "hypochlorous acid": 3.0e-8}
    Ca_values = np.logspace(-5, 0, 60)

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(11, 4.5))
    for (name, Ka), color in zip(acids.items(), ["steelblue", "darkorange", "seagreen"]):
        Q_mass_action, Q_other = [], []
        for Ca in Ca_values:
            acid = WeakAcid(Ca=Ca, Ka=Ka)
            h = acid.h_concentration()
            A_minus = Ka * Ca / (Ka + h)  # from the mass balance and Ka
            HA = Ca - A_minus
            Q_mass_action.append(h * A_minus / HA)
            Q_other.append(h / HA)
        ax1.loglog(Ca_values, Q_mass_action, color=color, label=name)
        ax1.axhline(Ka, color=color, linestyle=":", alpha=0.6)
        ax2.loglog(Ca_values, Q_other, color=color, label=name)

    ax1.set_xlabel("total acid concentration $C_a$ (mol/L)")
    ax1.set_ylabel(r"$[H^+][A^-]/[HA]$")
    ax1.set_title("Mass-action quotient: constant = $K_a$")
    ax1.legend(fontsize=8)
    ax2.set_xlabel("total acid concentration $C_a$ (mol/L)")
    ax2.set_ylabel(r"$[H^+]/[HA]$")
    ax2.set_title("A non-mass-action ratio: not constant")
    fig.tight_layout()




.. image-sg:: /api/gallery/solutions/acid_base/images/sphx_glr_plot_02_law_of_mass_action_001.png
   :alt: Mass-action quotient: constant = $K_a$, A non-mass-action ratio: not constant
   :srcset: /api/gallery/solutions/acid_base/images/sphx_glr_plot_02_law_of_mass_action_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 55-58

The exact solver never imposes the quotient directly -- it solves a
cubic from mass balance, charge balance, and water autoionization -- yet
the recovered quotient matches :math:`K_a` to rounding error:

.. GENERATED FROM PYTHON SOURCE LINES 58-65

.. code-block:: Python


    acid = WeakAcid(Ca=0.010, Ka=1.8e-5)
    h = acid.h_concentration()
    A_minus = acid.Ka * acid.Ca / (acid.Ka + h)
    print(f"[H+][A-]/[HA] = {h * A_minus / (acid.Ca - A_minus):.6e}  (Ka = {acid.Ka:.6e})")

    plt.show()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [H+][A-]/[HA] = 1.800000e-05  (Ka = 1.800000e-05)





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.164 seconds)


.. _sphx_glr_download_api_gallery_solutions_acid_base_plot_02_law_of_mass_action.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_law_of_mass_action.ipynb <plot_02_law_of_mass_action.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_law_of_mass_action.py <plot_02_law_of_mass_action.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_law_of_mass_action.zip <plot_02_law_of_mass_action.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_